5.3: Solving Quadratic Equations by Finding the Square Root Objectives: Students will be able to… Write a square root radical in simplest form Solve a quadratic equation by finding the square root

RADICALS The whole expression is called a radical. If r 2 = s: r is the square root If s is positive, it has 2 square roots: 3 2 =9 3, -3 Radical sign Radicand (# under radical sign)

If the radicand is not a perfect square, you can simplify it using properties of square roots. Product Property: To Simplify: Break radicand down into 2 factors (one MUST be the highest perfect square factor other than 1) Split into 2 radicals Simplify If no perfect square factor, the radical is in simplest form

Examples: Simplify: You can only multiply 2 numbers if they are both under a radical or both outside the radical!!

Simplify:

Quotient Property Technically, a radical is not in simplest form if you have a fraction under the radical or a radical in the denominator. To get rid of a radical in denominator, we rationalize the denominator.

Examples: Simplify:

Examples: Simplify

You can use square roots to solve some types of quadratics. One type is if there is no linear term: ax 2 +c=0 Remember…if x 2 = s, then x=± Two roots!!!!

Solve: a.) Isolate the squared expression b.) Take the square root of both sides. Don’t forget ± !!!

Solve:

You can check your answers by substituting answer back into original problem, or graph and find x-intercepts!!

Solve…why does this look different?? 3(x-2) 2 =21 Isolate squared expression first: Take square root of both sides: Set up 2 equations:

Solve:

When an object is dropped, the height, h (in feet) of an object at any time t (in seconds) is modeled by : Initial height

The tallest building in the U.S. is in Chicago. It is 1450 ft. tall. a.) How long would it take a penny to drop from the top of the building? b.) How fast would the penny be traveling when it hits the ground if the speed is given by s=32t where t is the number of seconds since the penny was dropped.

How long will it take an object dropped from a 550 ft tall tower to land on the rood of a 233 ft tall building?